Field Guard Stability Certificate and White Paper — REAL-E3 Systems (WP-FG-002)

Finnish patent application no. 20265235, filed 11.03.2026, REAL E3 Systems Oy. Field Guard is a mathematically certified stability layer for conversational AI governance systems, developed by REAL E3 Systems Oy (Finland, 2026). This record contains two documents: Stabilizer Core Certificate v3.0 — a formal ISS (Input-to-State Stability) certificate establishing bounded state admissibility via a normal-matrix Lyapunov construction. The analytic contraction argument closes cleanly using a rotation-scaling matrix variant that makes the Lyapunov matrix proportional to identity (P = 20I), eliminating norm consistency gaps entirely. Independently reviewed and verified. White Paper WP-FG-002 — full mathematical exposition of the Field Guard stability architecture, including spectral radius analysis, contraction proof, and ISS gain bounds. Integration Example: Field Guard sits between LLM output and system state in a conversational AI deployment. The 6D control vector governs activation, coherence, grounding, boundary enforcement, action readiness, and pace. Field Guard certifies that this vector remains within provably safe bounds at every transition. State admissibility is established — authority validation at irreversible execution boundaries is the next architectural layer. Scope: Field Guard v1 governs state stability. It does not currently implement authority re-validation at execution boundaries. That is an explicitly scoped next layer. Independently reviewed by Gregor Wegener, Independent Systems Architecture Analyst (AI Infrastructure Efficiency, Runtime Coherence & Agentic Systems Diagnostics).